Question

Длина основания прямоугольного параллелепипеда равна 43,2дм.а ширина в 1,8 раза меньше длины.Высота параллелепипеда в 3 раза меньше длины основания.Найти площадь полной поверхности,объём и сумму всех рёбер параллелепипеда.Найти площадь и объём куба у которого сумму длинн всех рёбер равна сумме всех измерений параллелепипеда

Answer 1

Х -ширина5х -высота1,4х -длинах*5х*1,4х=56х³=56/7=8х=2 -ширина10 -высота2,8 -длинаSпол=2*2,8*2+2*(2+2,8)*10=107,2 дм²

Answer 2

Given Information

- Length of the base of the rectangular parallelepiped: 43.2 dm - Width is 1.8 times smaller than the length - Height is 3 times smaller than the length of the base

Calculating the Width and Height

To find the width and height of the rectangular parallelepiped, we can use the given information that the width is 1.8 times smaller than the length, and the height is 3 times smaller than the length.

Let's calculate the width and height:

- Width = 1.8 * Length - Height = 3 * Length

Substituting the given length of the base (43.2 dm) into the formulas, we get:

- Width = 1.8 * 43.2 dm - Height = 3 * 43.2 dm

Calculating the width and height:

- Width = 77.76 dm - Height = 129.6 dm

Calculating the Surface Area

The surface area of a rectangular parallelepiped can be calculated using the formula:

Surface Area = 2 * (Length * Width + Length * Height + Width * Height)

Substituting the values we calculated earlier, we get:

Surface Area = 2 * (43.2 dm * 77.76 dm + 43.2 dm * 129.6 dm + 77.76 dm * 129.6 dm)

Calculating the surface area:

Surface Area = 2 * (3359.232 dm² + 5604.48 dm² + 10062.1056 dm²) = 2 * 19025.8176 dm² = 38051.6352 dm²

Therefore, the surface area of the rectangular parallelepiped is 38051.6352 dm².

Calculating the Volume

The volume of a rectangular parallelepiped can be calculated using the formula:

Volume = Length * Width * Height

Substituting the values we calculated earlier, we get:

Volume = 43.2 dm * 77.76 dm * 129.6 dm

Calculating the volume:

Volume = 432000 dm³

Therefore, the volume of the rectangular parallelepiped is 432000 dm³.

Calculating the Sum of All Edges

The sum of all edges of a rectangular parallelepiped can be calculated using the formula:

Sum of All Edges = 4 * (Length + Width + Height)

Substituting the values we calculated earlier, we get:

Sum of All Edges = 4 * (43.2 dm + 77.76 dm + 129.6 dm)

Calculating the sum of all edges:

Sum of All Edges = 4 * 250.56 dm = 1002.24 dm

Therefore, the sum of all edges of the rectangular parallelepiped is 1002.24 dm.

Calculating the Area and Volume of a Cube

To find the area and volume of a cube, we need to know the sum of the lengths of all edges of the cube. In this case, the sum of the lengths of all edges of the cube is equal to the sum of all measurements of the rectangular parallelepiped.

Let's calculate the area and volume of the cube:

- Sum of lengths of all edges of the cube = Sum of all measurements of the rectangular parallelepiped = 1002.24 dm

The length of each edge of the cube can be calculated by dividing the sum of lengths of all edges by 12 (since a cube has 12 edges):

- Length of each edge of the cube = Sum of lengths of all edges / 12 = 1002.24 dm / 12

Calculating the length of each edge of the cube:

- Length of each edge of the cube = 83.52 dm

Calculating the Area of the Cube

The area of a cube can be calculated using the formula:

Area = 6 * (Length of each edge)^2

Substituting the length of each edge of the cube (83.52 dm) into the formula, we get:

Area = 6 * (83.52 dm)^2

Calculating the area of the cube:

Area = 34992.82944 dm²

Therefore, the area of the cube is 34992.82944 dm².

Calculating the Volume of the Cube

The volume of a cube can be calculated using the formula:

Volume = (Length of each edge)^3

Substituting the length of each edge of the cube (83.52 dm) into the formula, we get:

Volume = (83.52 dm)^3

Calculating the volume of the cube:

Volume = 584,336.803328 dm³

Therefore, the volume of the cube is 584,336.803328 dm³.

In summary: - The surface area of the rectangular parallelepiped is 38051.6352 dm². - The volume of the rectangular parallelepiped is 432000 dm³. - The sum of all edges of the rectangular parallelepiped is 1002.24 dm. - The area of the cube is 34992.82944 dm². - The volume of the cube is 584,336.803328 dm³.